Array Operations¶

Mathematical operations can be completed using NumPy arrays.

Scalar Addition¶

Scalars can be added and subtracted from arrays and arrays can be added and subtracted from each other:

import numpy as np

a = np.array([1, 2, 3])
b = a + 2
print(b)

[3 4 5]

a = np.array([1, 2, 3])
b = np.array([2, 4, 6])
c = a + b
print(c)

[3 6 9]

Scalar Multiplication¶

NumPy arrays can be multiplied and divided by scalar integers and floats:

a = np.array([1,2,3])
b = 3*a
print(b)

[3 6 9]

a = np.array([10,20,30])
b = a/2
print(b)

[ 5. 10. 15.]

Array Multiplication¶

NumPy array can be multiplied by each other using matrix multiplication. These matrix multiplication methods include element-wise multiplication, the dot product, and the cross product.

Element-wise Multiplication¶

The standard multiplication sign in Python * produces element-wise multiplication on NumPy arrays.

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
a * b

array([ 4, 10, 18])

Dot Product¶

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
np.dot(a,b)

Cross Product¶

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])
np.cross(a, b)

array([-3,  6, -3])

Exponents and Logarithms¶

np.exp()¶

NumPy’s np.exp() function produces element-wise \(e^x\) exponentiation.

a = np.array([1, 2, 3])
np.exp(a)

array([ 2.71828183,  7.3890561 , 20.08553692])

Logarithms¶

NumPy has three logarithmic functions.

np.log() - natural logarithm (log base \(e\))
np.log2() - logarithm base 2
np.log10() - logarithm base 10

np.log(np.e)

1.0

np.log2(16)

4.0

np.log10(1000)

3.0

Trigonometry¶

NumPy also contains all of the standard trigonometry functions which operate on arrays.

np.sin() - sin
np.cos() - cosine
np.tan() - tangent
np.asin() - arc sine
np.acos() - arc cosine
np.atan() - arc tangent
np.hypot() - given sides of a triangle, returns hypotenuse

import numpy as np
np.set_printoptions(4)

a = np.array([0, np.pi/4, np.pi/3, np.pi/2])
print(np.sin(a))
print(np.cos(a))
print(np.tan(a))
print(f"Sides 3 and 4, hypotenuse {np.hypot(3,4)}")

[0.     0.7071 0.866  1.    ]
[1.0000e+00 7.0711e-01 5.0000e-01 6.1232e-17]
[0.0000e+00 1.0000e+00 1.7321e+00 1.6331e+16]
Sides 3 and 4, hypotenuse 5.0

NumPy contains functions to convert arrays of angles between degrees and radians.

deg2rad() - convert from degrees to radians
rad2deg() - convert from radians to degrees

a = np.array([np.pi,2*np.pi])
np.rad2deg(a)

array([180., 360.])

a = np.array([0,90, 180, 270])
np.deg2rad(a)

array([0.    , 1.5708, 3.1416, 4.7124])